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Optimization of a Dynamic Profit Function using Euclidean Path Integral

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  • P. Pramanik
  • A. M. Polansky

Abstract

A Euclidean path integral is used to find an optimal strategy for a firm under a Walrasian system, Pareto optimality and a non-cooperative feedback Nash Equilibrium. We define dynamic optimal strategies and develop a Feynman type path integration method to capture all non-additive convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, under Walrasian system we are able to solve for the optimal strategy under a linear constraint with a linear objective function with respect to strategy.

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  • P. Pramanik & A. M. Polansky, 2020. "Optimization of a Dynamic Profit Function using Euclidean Path Integral," Papers 2002.09394, arXiv.org.
    • Handle: RePEc:arx:papers:2002.09394
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    References listed on IDEAS

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    1. Chow, Gregory C., 1996. "The lagrange method of optimization with applications to portfolio and investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 1-18.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Bruce C. Greenwald & Joseph E. Stiglitz, 1986. "Externalities in Economies with Imperfect Information and Incomplete Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(2), pages 229-264.
    4. Jean-Philippe Bouchaud & Didier Sornette, 1994. "The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes," Science & Finance (CFM) working paper archive 500040, Science & Finance, Capital Fund Management.
    5. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, April.
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    Cited by:

    1. Md. Fazlul Huq Khan & Md. Masum Billah, 2023. "Macroeconomic factors and Stock exchange return: A Statistical Analysis," Papers 2305.02229, arXiv.org.

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